Mechanics

# Difference between density,mass and volume with examples

Mass and density are two physical quantities.Mass is the quantity of matter of an object while density is mass per unit volume.They are two different quantities but these quantities have relationships with each other, higher will be the mass higher will be the density.

Now!

We are going learn in detail about mass and density.

## What is mass?

The mass of an object is the measure of the amount of matter in it.The SI unit for mass is the kilogram.

The original kilogram prototype, which is a metal cylinder made of platinum and iridium, is kept in France.In Singapore, you can find a standard kilogram which is a copy of the original one, kept at the Singapore Institute of standards and industrial research.This copy is kept at reference for comparison.

Large masses are measured in tonnes while small masses are measured in grams or milligrams.Such as:

• Each grain of rice has a mass of about 0.02 mg.
• An apple has a mass of about 40 g.
• An elephant may weight about 4 tonnes.

Mass should not be confused with weight, although in daily life, we sometimes use them interchangeably.The mass of a substance depends on the number and size of particles which make up that substance.It cannot be changed by the location and shape of the substance.

For example, a lump of plasticine having a mass of 100 g will still have the same mass even if it is made into the shape of a boat.

## How can we measure mass?

We use a balance to measure mass.A beam balance is still used to give very accurate measurements.However, the electronic balance is fast becoming popular due to its easy handling, high accuracy, and easy digital reading.You will learn to identify the different types of balances and use the beam balance to measure mass.

## What is Density?

Which is heavier -wood or iron?

A piece of iron has a greater mass than a piece of wood provided both have the same volume.In other words, iron has a higher density than wood.

“Mass per unit volume  of a material is called density.”Density is an important property of any material.A homogeneous material such as ice or iron has the same density throughout.We use  (the Greek letter rho) for density.If a mass m of homogeneous material has volume V , the density  is: Two objects made of the same material have the same density even though they may have different masses and different volumes.That’s because the ratio of mass to volume is the same for both objects.

## Units for Density

The S.I unit of density is the kilogram per cubic meter (1kg/m3).The cgs unit, the gram per cubic centimeter (1g/cm3), is also widely used:

1g/cm3=1000 1kg/m3

The densities of several common substances at ordinary temperatures are given in the table.

The densest material found on earth is the metal osmium (22,500 kg/m3), but its density pales in comparison to the densities of exotic astronomical objects such as white dwarf stars and neytron stars.

## How to find the density of a substance?

We can measure the density of a substance in two steps.

1. Measure the mass and volume of the substance.
2. Divide the mass of the substance by its volume.The result gives the density of the substance.

Density = Mass / Volume

Or

Mass = Density × volume

For example:

Osmium, the densest metal found, has a density of 22.6 g/cm³.The mass of a block of osmium was found to be 113 g.Find its volume.

Sol:

The volume of the block of osmium = Mass /Density

= 113 g/22.6 g/cm³

=5  cm³

## Floating and Sinking

Have you ever wondered why some objects float, while others sink?

Objects such as a pebble or a ball bearing sink in water because they have a higher density than water will float.In general, substances with lower densities will float in substances with higher densities.

## Specific gravity

The specific gravity of a material is the ratio of its mass/volume to the mass/volume of water at 4.0c0,1000 kg/m3,it is a pure number without units.For example, the specific gravity of aluminum is 2.7.”Specific gravity” is a poor term , since it has nothing to do with gravity; relative density’ would have would have been better.

The mass/volume of some materials varies from point to point within the material.One example is the material of the human body, which includes low-density fat (about 940 kg/m3) and high-density bone (from 1700 to 2500 kg/m3).Two others are the earth’s atmosphere (which are denser at greater depths).For these materials equation (1) describes the average density.In general, the density of a material depends on environmental factors such as temperature and pressure.

Measuring mass/volume is an important analytical technique.For example,we can determine the charge condition of a storage battery by measuring the density of its electrolyte,a sulphuric acid solution.As the battery discharges ,the sulfuric acid combines with lead in the battery plates to form insoluble lead sulfate,decreasing the concentration of the solution.The density decreases from about 1.30 3 kg/m3 for a fully charged battery to 1.15 3 kg/m3 for a discharged   battery.

Another automotive example is permanent type antifreeze,which is usually a solution of ethylene glycol (3 kg/m3 ) and water.The freezing point of the solution depends on the glycol concentration,which can be performed by using a device called a hydrometer.